Hi LooseLarry,
You can view all of the content purchased in iTunes under a given Apple ID as follows:
Open iTunes and sign on with the Apple ID that you wish to view purchases for
Click on the iTunes Store
Click on Purchased under Quick Links on the right side of store window
Click on the tab that you wish to view purchases for (Music, Movies, etc.)
For Music, click on Songs and All to see all songs purchased under that Apple ID
The ones with the cloud next to them are not currently on your computer - they can be downloaded individually by clicking the cloud next to them, or en masse, by clicking Download All at the bottom
Cheers,
GB